The survey shows the Massachusetts Democrat trailing GOP Sen. Scott Brown by a single percentage point, with Brown netting 48 percent to Warren’s 47 percent. The result marks a measurable shift toward Warren since the last Suffolk poll in February, which had Brown up 9 points, 49 percent to 40 percent.

The poll of 600 likely voters was in the field Sunday through Tuesday, more than three weeks after the Boston Herald first reported Warren’s Native American heritage listing at Harvard Law School when she was a professor there in the 1990s.

Since then, Warren has been ensnared in a round of unflattering stories questioning the credibility of her claim that she is 1/32 Cherokee.

Republicans had hoped the developing narrative would shred Warren’s credibility and knock her campaign off message.

While the latter has been accomplished to some degree, it appears the damage to her candidacy has been minimal.

A plurality of those polled — 49 percent — believe Warren is telling the truth about being part Native American. Just 28 percent said she was not being honest while 23 percent weren’t sure.

A plurality of 45 percent also believe she did not benefit by listing herself as a minority at Harvard or the University of Pennsylvania, where she also taught.

More than two-thirds of voters — 69 percent — said Warren’s Native American heritage listing is not a significant story, with just 27 percent saying it is.

Those numbers are likely to calm the fears of state Democrats but the poll isn’t all bad news for Brown.

His personal favorability is up 6 points in three months to 58 percent. Warren also saw her favorability rating increase (43 percent) but also saw her unfavorable rating (33 percent) rise 5 points since February.

Forty-seven percent said Brown would be an independent senator compared with 42 percent for Warren.

Polling director David Paleologos surmised that the battle over the next five months would be over a very small amount of undecided voters.

“This leaves both campaigns no choice but to spend tens of millions of dollars in an all-out war to woo the 5 percent of voters who will decide this election,” he said.

The Suffolk poll, which has a margin of error of plus or minus 4 percent, produced a result similar to an internal poll taken by the Democratic Senatorial Campaign Committee to quash speculation that Warren was hemorrhaging support due to the ancestry flap.

The DSCC survey, taken by Harstad Strategic Research May 8-10, resulted in a deadlocked race at 46 percent.

While Republicans argue that Brown has been outspent by Warren on advertising over the past month, Democrats are heartened by the pair of surveys showing the damage to their candidate to be minimal.

“When you look at the last month or so that Elizabeth Warren has had, you have to say she weathered the storm. The fact that she’s picked up 8 points shows she’s a better candidate than people think, a more resilient candidate than some would’ve thought,” said Boston-based Democratic strategist Mary Anne Marsh.